Method of recertifying a loaded bearing member

ABSTRACT

The present invention is a method of recertifying a loaded bearing member using ultrasound testing to compensate for different equipment configurations and temperature conditions. The standard frequency F1 of a reference block is determined via an ultrasound tone burst generated by a first pulsed phase locked loop (P2L2) equipment configuration. Once a lock point number s is determined for F1, the reference frequency F1a of the reference block is determined at this lock point number via a second P2L2 equipment configuration to permit an equipment offset compensation factor Fo1=((F1-F1a)/F1)(1000000) to be determined. Next, a reference frequency F2 of the unloaded bearing member is determined using the second P2L2 equipment configuration and is then compensated for equipment offset errors via the relationship F2c=F2+F2(Fo1)/1000000. A lock point number b is also determined for F2. A resonant frequency F3 is determined for the reference block using a third P2L2 equipment configuration to determine a second offset compensation factor Fo2 (=(((F1-F3)/F1) 1000000). Next the resonant frequency F4 of the loaded bearing member is measured at lock point number b via the third P2L2 equipment configuration and the bolt load determined by the relationship load=(-1000000)Cl(((F2C-F4)/F2C)- Fo2), wherein Cl is a factor correlating measured frequency shift to the applied load. Temperature compensation is also performed at each point in the process.

ORIGIN OF THE INVENTION

The invention described herein was made by an employee of the UnitedStates Government and may be manufactured and used by and for theGovernment for governmental purposes without the payment of anyroyalties thereon or therefor.

CROSS-REFERENCE

This application is related to a co-pending application entitled "Methodof Recertifying a Loaded Bearing Member Using a Phase Point", Ser. No.07/720,153, filed Jun. 19, 1991.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates generally to material testing and moreparticularly to a method of recertifying the load on a bearing membervia ultrasound techniques.

2. Discussion of the Related Art

The pulsed phase locked loop strain monitor, or P2L2, is a device whichcan be utilized to nondestructively measure the load in a bearing membersuch as a bolt, connector, etc. The P2L2, described in U.S. Pat. No.4,363,242 to Heyman, measures acoustic phase changes and displaysfrequency changes which are indicative of changes in the load of thebearing member. By only determining load changes, the P2L2 requires thatthe ultrasonic sensor be kept on the bearing member during tightening orother load applications. Measurement of the load in a tightened bearingmember, i.e., load recertification, is not possible because temperaturevariations as well as substitutions of various P2L2 elements such astransducers, cables, ultrasonic bonding, coupling, the P2L2 memberitself, etc. are not corrected for a subsequent, after load measurement.In addition, it is often difficult to return to the same frequency pointto correctly determine a subsequent frequency shift, thereby resultingin incorrect load determination.

Other non-destructive load testing systems include using an ultrasonicmonitor to measure the time of flight of ultrasonic waves through abolt. This measured time of flight is indicative of bolt loading. Suchtime of flight systems are harder to use and generally less accuratethan P2L2 systems because the correct threshold trigger point must beselected to give the correct load measurement. In addition, loadrecertification of an already tightened bearing member is difficult forthe reasons discussed above in connection with the P2L2 system.

OBJECTS OF THE INVENTION

It is accordingly an object of the present invention to permit loadrecertification of a loaded bearing member.

It is another object of the present invention to accomplish theforegoing object while accounting for changes in temperature.

It is a further object of the present invention to accomplish theforegoing objects while permitting substitutions of various P2L2 systemcomponents and recertification subsystem components.

It is another object of the present invention to avoid the difficultiesand incorrect load determination associated with returning to afrequency peak lock point number after a period of time has elapsed.

It is yet another object of the present invention to accomplish theforegoing objects non-destructively.

It is a further object of the present invention to accomplish theforegoing objects in a simple manner.

Additional objects and advantages of the present invention are apparentfrom the drawings and specification.

SUMMARY OF THE INVENTION

The foregoing and additional objects are achieved by a method forrecertifying the load of a bearing member according to the presentinvention. The standard frequency F1 of a reference block is determinedvia an ultrasound tone burst generated by a first pulsed phase lockedloop (P2L2) equipment configuration. Once a lock point number s isdetermined for F1, the reference frequency F1a of the reference block isdetermined at this lock point number via a second P2L2 equipmentconfiguration to permit an equipment offset compensation factorFo1=((F1-F1a)/F1) (1000000) to be determined. Next, a referencefrequency F2 of the unloaded bearing member is determined using thesecond P2L2 equipment configuration and is then compensated forequipment offset errors via the relationship F2c=F2+F2(Fo1)/1000000. Alock point number b is also determined for F2. A resonant frequency F3is determined for the reference block using a third P2L2 equipmentconfiguration to determine a second offset compensation factorFo2(=(((F1-F3)/F1) 1000000). Next the resonant frequency F4 of theloaded bearing member is measured at lock point number b via the thirdP2L2 equipment configuration and the bolt load determined by therelationship bolt load=(-1000000)CI(((F2c-F4)/F2c)-Fo2), wherein CI is afactor correlating measured frequency shift to the applied load.Temperature compensation is also performed at each point in the process.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of the constituent elements of a prior artpulsed phase locked loop strain monitor;

FIG. 2 is a schematic diagram of a prior art pulsed phase locked loopstrain monitor and associated hardware;

FIG. 3 is a schematic diagram of a pulsed phase locked loop equipmentconfiguration according to the present invention;

FIG. 4 is a graph showing the correlation of the frequency shift ΔF/Fwith bolt load;

FIG. 5 is a graph schematically depicting a typical ultrasonic frequencyspectrum of a bearing member showing the lock point for a loaded andunloaded bolt and the load-induced frequency shift of a typical lockpoint;

FIG. 6 is a graph showing the correlation of the frequency shift withtemperature;

FIG. 7 is a graph depicting the frequency spacing of successive lockpoints for a loaded and unloaded bolt;

FIGS. 8a and 8b show the P2L2 output pulse and phase signals forunlocked and locked conditions as displayed on an oscilloscope;

FIG. 9 is a graph showing the relationship between bolt load and lockpoint spacing; and

FIG. 10 is a graph showing the relationship between lock point spacingand temperature.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, a pulse phase locked loop strain monitor or P2L2 10is schematically shown. The P2L2 is described in greater detail in U.S.Pat. No. 4,363,242 to Heyman, the specification of which is herebyincorporated by reference. The P2L2 measures acoustic phase change andreads out corresponding frequency changes. In general terms, the RFoutput of a voltage controlled oscillator (VCO) 12 is periodically gatedby gate 14 and then amplified and transmitted via amplifier transmitter16 to an ultrasonic transducer 18. Transducer 18 is affixed to an end oftest material 20 via an appropriate couplant 19 such as water, glycerin,light machine oil, etc. and produces an acoustic tone burst or soundwave pulse which propagates in bearing member 20. The produced acousticsignal may have any ultrasonic frequency near the center of theoperating frequency bandwidth of the compound resonator formed by thetransducer bonded to the load bearing member. Also, test material 20 maybe a load bearing member such as a bolt or other load bearing componentof any geometrical configuration.

The generated tone burst or sound wave pulse is reflected by the far endof test material 20 back to transducer 18 and converted to an electricalsignal by the transducer. The signal is gated by gate 22, amplified byamplifier receiver 24, and sent to mixer phase detector 26. Mixer phasedetector 26 also receives the output of VCO 12 and produces a DC signalproportional to the phase difference between these two inputs. Logictiming system 28 controls the gating time of gates 14 and 22 in responseto a signal received from VCO 12. Logic timing system 28 also controlsthe time at which a phase point of the phase difference signal issampled and held by sample/hold circuit 30. This sampled signal is thenappropriately conditioned by signal conditioner 32 and sent to VCO 12 tocontrol the VCO output frequency. The P2L2 locks onto resonantfrequencies which correspond to quadrature which represents a phasedelay of 2πN+φ_(o), where N is an integer and φ_(o) is typically 90°.

Once the frequency F is locked at a particular lock point, any deviationin the propagation length or sound velocity of the test material 20results in a frequency change ΔF needed to maintain a fixed phasecondition. Thus, the P2L2 10 measures frequency changes to indicate loadchanges, i.e., tension or compression, which change the sound velocityand propagation length. This frequency change relationship (ΔF/F)resulting from the load change is interpreted via a load-member-specificultrasonic load calibration factor CI, which is defined in units oflb/ppm to indicate pounds of load change per parts per million ofnormalized frequency shift. The factor CI is determined by obtainingfrequency changes resulting from loads for the particular bearing memberand obtaining a polynomial function which represents an acceptable curvefit for the obtained data. For simplicity, a first order linearpolynomial is generated and the x-coefficient representing the slope ofthe curve is expressed as CI. Then when the load is changed, thenormalized frequency shift is multiplied by the CI factor to determinethe load change. See FIG. 4.

If the load is the only parameter changed, then the displayed frequencychange is indicative solely of this load change. However, changes inother parameters such as equipment and temperature may also affect thefrequency changes, thereby contaminating the subsequent load changedetermination. Compensation must accordingly be made for these otherparameter changes. Changes in the measurement equipment configurationtypically occur over the period of time between the initial andsubsequent measurements as specific components are replaced due to loss,failure or interchangement with other configurations. Also, temperaturefluctuations can have significant effects; e.g., a 1° F. change canresult in a frequency change which would incorrectly indicate a 350 lb.load change in a shuttle wheel bolt.

As shown in FIG. 2, an oscilloscope 34 and a frequency counter 36 areconnected to P2L2 10 to provide a respective visual display and anelectronic readout of the VCO 12 frequency (FIG. 1). Test material 20,e.g., a bolt, is passed through a load cell 38 and has a nut 40 threadedon the end opposite transducer 18 which is tightened to induce a load.Alternatively, the transducer can be coupled to the nut end of the bolt.Load cell 38 duplicates the actual field thickness where the bolt is tobe installed. A voltmeter 42 reads the voltage induced in load cell 38by the tightening of nut 40. Alternatively, the load can be measured bya hydraulic or other type of indicator. The outputs of voltmeter 42 andfrequency counter 36 are read by computer 44 as nut 40 is tightened.This data is fed to an appropriate printer/plotter 46 for display.

The method and system for testing load bearing members according to thepresent invention will now be described with particular reference toFIGS. 3 and 4. Prior to performing any load measurement of bearingmember 20, the particular equipment configurations, e.g., P2L2 10,transducer 18, connecting cable 48, couplant 19, etc., for detecting theVCO frequency changes is selected. This configuration, designedconfiguration A, is connected to reference or calibration block 50 asindicated by the dotted line indicating cable 48 in FIG. 3. In addition,a thermometer 52 is connected to reference block 50 via cable 54, asindicated by the dotted line 54 in FIG. 3. Of course, the thermometermay be hand-held and read. The following standard measurements anddeterminations are obtained for reference block 50:

(1) measuring the standard lock point frequency F1 (Hz) via theparticular transducer 18, cable 48, couplant, and P2L2 10 ofconfiguration A;

(2) measuring the temperature T1 (°F) via thermometer 52 and cable 54;

(3) determining the calibration standard lock point number s; and

(4) determining the reference block ultrasonic thermal calibrationfactor Ctr (ppm/°F).

Step (3) involves measuring the frequency separation or spacing betweentwo successive lock points at temperature T1 and then dividing F1 bythis measured spacing. Each lock point is a mechanical resonantfrequency of the calibration block 50. In FIG. 5 the general case isillustrated wherein the lock point number is represented by m and themechanical resonant frequencies are represented by peaks. Thefundamental resonant frequency corresponds to m=1 and the mth harmonicresonant frequency is represented by the mth peak in FIG. 5. The valueof m is generally equal to F/ (F_(m+1) -F_(m)), and s is specificallyequal to F1/(F_(s+1) -F_(s)), wherein F_(s) and F_(s+1) are any twosuccessive harmonic frequencies. The determination of the lock pointnumber m or s allows the P2L2 to return to the same frequency peak afteran induced load to determine the true load-induced frequency shift. Thesame lock point number must be used because often this frequency shiftis greater than the harmonic interval or lock point spacing andaccordingly merely using the frequency F1 to recertify the load couldresult in a significant misreading of the frequency change. The lockpoint number is optimally chosen so that the frequencies lie near thecenter of the operating frequency bandwidth of the compound resonatorformed by the transducer 18 bonded to the load bearing member 20 by thecouplant 19.

The determination of the material specific Ctr in step (4) involves useof an experimentally derived relationship between the change in resonantor harmonic frequency and temperature, i.e., a shift in the lock point sand the change in temperature, as generally represented in FIG. 6. Forexample, the reference block may be placed in an oven and its frequencyobserved at various temperatures. Like CI, Ctr represents the slope of alinear or other polynomial function which best fits the generated datacurve.

Next, another equipment configuration comprising at least one element,and as many as all elements, different from the corresponding elementsin configuration A is selected for determining the VCO frequencychanges. This other configuration, designated configuration B, is alsoconnected to reference block 50 as indicated by the dotted lines in FIG.3 prior to performing any load measurement of bearing member 20. If anyelement is changed in the configuration, the true propagation pathlength also changes, resulting in all of the lock point frequenciesbeing shifted by approximately the same amount. Similarly, a temperaturechange can also shift the lock point frequencies. Equipment offseterrors are obtained for configuration B by the following steps:

(5) measuring the reference block lock point frequency F1a (Hz) via theparticular transducer 18, cable 48, couplant and P2L2 10 ofconfiguration B using lock point number s;

(6) measuring the reference block temperature T1a (°F.) via thermometer52 and cable 54;

(7) compensating F1a for temperature difference T1-T1a using Ctr suchthat

    F1ac=F1a-Ctr(T1-T1a)F1/1000000,

wherein F1ac is compensated F1a; and

(8) determining the dimensionless offset compensation factor Fo1expressed in parts of frequency shift per million parts of operatingfrequency:

    Fo1=((F1-F1ac)/F1)1000000,

to allow compensation for the difference in resonant frequenciesdetermined from using two different equipment configurations. If nocompensation is made for the temperature-induced frequency change, F1ais substituted for F1ac in the preceding equations.

Still using equipment configuration B, the transducer 18 and thermometer52 are then connected to bearing member 20 and the followingmeasurements obtained:

(9) measuring the reference lock point frequency F2 (Hz) of the unloadedbolt (bearing member 20) via the particular transducer 18, cable 48,couplant and P2L2 10 of configuration B;

(10) measuring the unloaded bolt reference temperature T2 (°F.) viathermometer 52 and cable 54;

(11) determining the bolt lock point number b by measuring the frequencyseparation or spacing between two lock points and dividing this spacinginto F2 as described above in reference to lock point number s;

(12) compensating the unloaded bolt reference frequency for equipmentoffset errors with the previously determined reference block offsetcompensation factor Fo1 (step 8) by

    F2c=F2+F2(Fo1)/1000000,

wherein F2c is the compensated frequency;

(13) determining the bolt ultrasonic load calibration factor CI (lb/ppm)as discussed above; and

(14) determining the material specific, bolt ultrasonic thermalcalibration factor Ct (ppm/°F.) using the experimentally derivedrelationship between the normalized shift of lock point frequency numberb and the change in temperature as generally shown in FIG. 6 tocompensate for any subsequent temperature deviation from the initialbolt temperature T2. Ct may be determined by the same method as Ctr.

Once all of the measurements and determinations are made in steps(1)-(14), the bearing member 20, e.g., a bolt, is installed under load(preloaded) in a field condition rather than in the approximating loadcell 38. In all likelihood, the tester would prefer the widest possiblelatitude in selecting the particular equipment configuration todetermine the load indicating VCO frequency changes at the particulartest time due to equipment repair, replacement and availability. A newconfiguration C having at least one element and possibly all elements,different from the corresponding elements in configurations A and B, isselected. Also, the effects of a different temperature at test time fromthe initial measurements must be taken into account. As statedpreviously, it is paramount to know which lock point number of thebearing member is being used for the measurement in order to assess theload on the load bearing member with any equipment and temperaturechanges. Configuration C is accordingly connected to reference block 50to obtain the following measurements and error corrections using lockpoint number s:

(15) measuring the reference block lock point frequency F3 (Hz) at lockpoint number s via the particular transducer 18, cable 48, couplant andP2L2 10 of configuration C;

(16) measuring the reference block temperature T3 (°F.) via thermometer52 and cable 54;

(17) compensating F3 for temperature difference T1-T3 using Ctr by thefollowing:

    F3c=F3-Ctr(T1-T3)F1/1000000,

wherein F3c is the temperature compensated frequency F3; and

(18) calculating the offset compensation Fo2 by

    Fo2=((F1-F3c)/F1)1000000.

If no compensation is made for the temperature-induced frequency change,F3 is substituted for F3c in the preceding equation. Finally, the loadedbolt at the test site is connected to configuration C and the followingsteps taken:

(19) measuring the bolt frequency F4 (Hz) at lock point b via theparticular transducer 28, cable 48, couplant and P2L2 10 ofconfiguration C;

(20) measuring the bolt temperature T4 (°F.) via thermometer 52 andcable 54;

(21) compensating F4 for temperature difference T2-T4 using Ct (derivedin step 14) by the following:

    F4c=F4-Ct(T2-T4)F2C;

wherein F4c is the temperature compensated frequency F4; and

(22) determining the true load:

    load=(-1000000)CI(((F2c-F4c)/F2c)-Fo2).

If no compensation is made for the temperature-induced frequency change,F2 and F4 are respectively substituted for F2c and F4c in the precedingequation. In practice, numerous bolts could be measured at one timeduring steps (5)-(14) using equipment configuration B to determine therespective compensated bolt reference frequencies and temperatures.Steps (1)-(4) relating to the calibration reference block 50 need onlybe performed once regardless of the number of bolts tested. Steps(15)-(22) are performed as desired to recertify this bolt load with theparticular contemporaneous equipment configuration C and temperature T3.

As noted previously, both the lock point number s for reference block 50and lock point number b for bearing member 20 can be determined bymeasuring the frequency spacing between respective successive lockpoints at a particular temperature and then dividing this frequencyspacing into the frequency of the particular element at thistemperature. The subsequent lock point frequencies are then determinedby multiplying the lock point number by a subsequently measured spacingbetween two successive lock points.

Another method will now be described to allow one to subsequently obtainthe same lock point in order to perform recertification of a load by thesame equipment configuration. This method locks at the same phase pointon the acoustic signal done visually using an oscilloscope andduplicating the sample/hold (S/H) setting N on the P2L2. As shown inFIGS. 5 and 7, a frequency F_(m) defines an amplitude or resonant peakwherein F_(m) =mV/2L, wherein m is the harmonic number, V is thevelocity of the acoustic tone burst through the bearing member, and L isthe length of the bearing member through which the acoustic tone bursttravels. The number of wavelengths λ in the bolt path is 2L/λ, wherein2L is the round-trip or two-way length of the propagation path in thebolt. The number of wavelengths in the bearing member is thus equal to2LF_(m) /V, which is equal to F_(m) T, wherein T is the time requiredfor propagation along the bolt and back. Thus, N represents a specificpoint in phase that is determined by the bolt length, frequency andvelocity.

Referring to FIGS. 8a and 8b, in operation a certain P2L2 S/H setting Nis selected as shown in FIG. 8a, then the P2L2 is locked so that it isin quadrature as shown in FIG. 8b to drive the phase signal to zeroinitially for a no load condition and the wave number w in the toneburst where the S/H marker appears is noted. For example, w is theintegral number of the third wave counting from left to right in FIG.8b. The initial temperature, S/H setting N and wave number w arerecorded. When the bearing member is tightened to induce a load with theP2L2 locked as shown in FIG. 8b, the frequency and the phase samplepoint both will shift by an amount equal to the shift in time caused bythe bolt tension. If, after the bolt is loaded, the measurement systemis removed from the bolt causing loss of the original P2L2 lock and thenthe system is reinstalled to recertify load later on, re-locking withoutchanging any of the P2L2 settings may result in relock at a differentlock point and will imply an incorrect load. To avoid any misreading,the S/H setting N on the P2L2 is duplicated and the P2L2 VCO frequencyis adjusted with the P2L2 unlocked until the S/H marker is at the samewave number w on the acoustic signal as during the initial measurement.The P2L2 is then locked at the wth wave to provide a valid measurementof the frequency for determination of bolt load using this frequency forthe final frequency and the particular CI. In addition, the finaltemperature is measured and any temperature-induced frequency changecompensated for using this temperature, the initial temperature, and athermal calibration factor as discussed above.

In addition to duplicating the sample/hold setting, the tone bursttransmission width and pulse repetition rate should also be duplicatedand the measurement should be made on the same echo number (i.e., firstecho=first reflection from back surface of bearing member, secondecho=second reflection, etc.).

An alternate approach to load recertification will now be explained. Theprevious two methods measure the frequency shift of a lock point, i.e.,ΔF, to determine the load as a function of ΔF/F. This approach, on theother hand, measures the change in frequency spacing between two lockpoints as a function of bolt load. As illustrated in FIGS. 7 and 9, asbolt load increases the spacing between two successive lock pointsdecreases. Lock point spacing is measured using an oscilloscope toobserve the P2L2 signals by first locking to a lock point near thecenter of the operating frequency bandwidth of the compound resonatorformed by the transducer bonded to the load bearing member by thecouplant, recording this original frequency, then unlocking the P2L2,adjusting the VCO frequency until 360° (2π) of phase shift has occurred,adjusting the S/H position back to the original phase point on theultrasonic signal, then re-locking the P2L2 and subtracting the newfrequency from the original frequency to determine spacing. Afterloading, the above steps are repeated to determine a subsequent lockpoint spacing.

Referring to FIG. 9, the lock point spacing changes as to a function ofload. A load calibration factor Cs may be determined as discussedpreviously for CI, wherein Cs is a part of a polynomial which representsan acceptable curve fit for the previously compiled load/frequencyspacing data. Thus, a determination of the frequency spacing leads to aload determination.

Referring now to FIG. 10, the lock point spacing also changes withtemperature. Accordingly, a thermal calibration factor Cst is determinedas discussed previously for Ct and Ctr, wherein Cst is a part of apolynomial which represents an acceptable curve fit for the previouslycompiled temperature/frequency spacing data. Thus, if an initialtemperature reading is taken substantially contemporaneously with theoriginal frequency spacing determination and a subsequent temperaturereading is taken substantially contemporaneously with the subsequentfrequency spacing determination, then a temperature compensation can beperformed on the reading as discussed previously.

The determinations and calculations of the above described values can becarried out by computer 44 employing appropriate software embodying themethodologies described above.

Many modifications, improvements and substitutions will be apparent tothe skilled artisan without departing from the spirit and scope of thepresent invention as described herein and defined in the followingclaims.

What is claimed is:
 1. A method of recertifying a load on a bearingmember using various pulsed phase locked loop (P2L2) equipmentconfigurations comprising the following elements of pulsed phase lockedloop system, transducer, ultrasonic couplant, and an interconnectingcable between the transducer and the system, each pulsed phase lockedloop system having an output frequency comprising the steps of:(a)performing the following steps on a reference block:(i) applying anultrasonic tone burst to the reference block via a first transducer of afirst P2L2 equipment configuration to determine the standard frequencyF1 of the reference block; (ii) determining a lock point number sindicative of a selected harmonic resonant frequency of the referenceblock; (iii) applying an ultrasonic tone burst to the reference blockvia a second transducer of a second P2L2 equipment configurationcomprising at least one element different from the elements of the firstequipment configuratio, to determine the resonant frequency F1a of thereference block at lock point s; (iv) determining a first dimensionlessoffset compensation factor Fo1 by the relationship

    Fo1=((F1-F1a)/F1)1000000;

(b) performing the following steps on the unloaded bearing member:(i)applying an ultrasonic tone burst to the unloaded bearing member usingthe second equipment configuration to determine the reference frequencyF2 of the unloaded bearing member; (ii) determining a lock point numberb indicative of a selected harmonic resonant frequency of the bearingmember; and (iii) compensating the unloaded bearing member frequency F2for equipment offset errors between the first and second equipmentconfigurations by the relationship F2c=F2+F2(Fo1)/1000000; wherein F2cis the compensated frequency; (c) performing the following steps on thereference block:(i) applying an ultrasonic tone burst to the referenceblock via a third equipment configuration having at least one elementdifferent from the first and second equipment configuration, todetermine a resonant frequency F3 at lock point number s of thereference block; and (ii) determining a second dimensionless offsetcompensation factor Fo2 by the relationship ((F1-F3)/F1)1000000; (d)performing the following steps on the bearing member after a load isapplied thereto:(i) applying an ultrasonic tone burst to the loadedbearing member via the third equipment configuration to determine aresonant frequency F4 (at lock point number b) of the loaded bearingmember; and (ii) determining the bolt load equal to (-1000000)Cl(((F2c-F4)/F2c)-Fo2), wherein Cl is a bearing member calibrationfactor correlating the measured frequency shift to the applied load. 2.The method according to claim 1, wherein step (a)(iii) comprisesdetermining the difference between two successive resonant frequenciesof the reference block and multiplying this by s to obtain a frequency,adjusting the P2L2 to this frequency and locking the P2L2 to measureF1a.
 3. The method according to claim 1, wherein step (b)(ii) comprisesdetermining the difference between two successive resonant frequenciesof the bearing member and dividing this difference into F2 to obtain b.4. The method according to claim 1, further comprising the steps ofmeasuring the temperature T1 of the reference block substantiallycontemporaneously with step (a)(i);measuring the temperature T1a of thereference block substantially contemporaneously with step (a)(iii); andcompensating frequency F1a for any change in temperature via therelationship F1a-Ctr (T1-T1a)F1/ 100000 prior to step (a)(iv), whereinCtr is a determined thermal calibration factor correlating temperaturechange and resonant frequency change in the reference block.
 5. Themethod according to claim 4, further comprising the steps of measuringthe temperature T2 of the unloaded bearing member substantiallycontemporaneously with step (b)(i);measuring the temperature T4 of theloaded bearing member substantially contemporaneously with step (d)(i);and compensating frequency F4 for any change in temperature via therelationship F4-Ct (T2-T4) F2c prior to step (d)(ii), wherein Ct is adetermined calibration factor correlating temperature change andresonant frequency change in the bearing member.
 6. The method accordingto claim 1, further comprising the steps of measuring the temperature T2of the unloaded bearing member substantially contemporaneously with step(b)(i);measuring the temperature T4 of the loaded bearing membersubstantially contemporaneously with step (d)(i); and compensatingfrequency F4 for any change in temperature via the relationship F4-Ct(T2-T4) F2c prior to step (d)(ii), wherein Ct is a determinedcalibration factor correlating temperature change and resonant frequencychange in the bearing member.
 7. The method according to claim 1,further comprising the steps of measuring the temperature T1 of thereference block substantially contemporaneously with step(a)(i);measuring the temperature T3 of the reference block substantiallycontemporaneously with step (c)(i); and compensating frequency F3 forany change in temperature via the relationship F3-Ctr(T1-T3)F1/1000000prior to step (c)(ii), wherein Ctr is a determined thermal calibrationfactor correlating temperature change and resonant frequency changes inthe reference block.
 8. A method of recertifying a load on a bearingmember comprising the steps of:(a) applying an ultrasonic tone burst tothe bearing member in an unloaded condition; (b) determining the spacingbetween two successive harmonic resonant frequencies of the unloadedbearing member; (c) applying an ultrasonic tone burst to the bearingmember in an undetermined loaded condition; (d) determining the spacingbetween two successive harmonic resonant frequencies of the loadedbearing member; and (e) computing the load on the bearing member basedon the difference in spacing between the unloaded and loaded conditions.9. The method according to claim 8, further comprising the steps of:(f)measuring the temperature of the unloaded bearing member substantiallycontemporaneously with step (b); (g) measuring the temperature of theloaded bearing member substantially contemporaneously with step (d); and(h) compensating for any temperature-induced change in the spacing usinga predetermined thermal correction factor and the difference between thetemperatures measured in steps (f) and (g).
 10. The method according toclaim 8, wherein the load on the bearing member is determined bymultiplying the difference in spacing between the unloaded and loadedcondition by a predetermined load calibration factor.